Question

solve for z.
2 > \frac{-3z - 2}{2} \geq -7
write your answer as a compound inequality with integers.

Explanation:

Step1: Multiply each part by 2

Multiply all three parts of the inequality $2>\frac{-3z - 2}{2}\geq - 7$ by 2 to get rid of the denominator.
$2\times2>\frac{-3z - 2}{2}\times2\geq - 7\times2$, which simplifies to $4>-3z - 2\geq - 14$.

Step2: Add 2 to each part

Add 2 to all three parts of the inequality $4>-3z - 2\geq - 14$.
$4 + 2>-3z-2 + 2\geq - 14+2$, resulting in $6>-3z\geq - 12$.

Step3: Divide each part by -3 and reverse the inequality signs

Divide all three parts of the inequality $6>-3z\geq - 12$ by - 3. Since we are dividing by a negative number, we reverse the inequality signs.
$\frac{6}{-3}<\frac{-3z}{-3}\leq\frac{-12}{-3}$, which simplifies to $-2

Answer:

$-2